David Joyce; Dept. of Mathematics & Computer Science, Clark University

Description:

The hyperbolic plane has more space in it then the Euclidean plane. There are only three regular tessellations of the Euclidean plane, namely {3,6} in which equilateral triangles meet six at each vertex, {4,4} in which squares meet four at each vertex, and {6,3} in which hexagons meet three at each vertex. But the hyperbolic plane can be tiled by any kind of regular polygon, and in many different ways... the Poincare Disk; regular tessellations; dual tessellations; quasiregular tessellations.